It is commonly necessary in control applications to determine the derivative of a measured input signal. In the control of a motor vehicle transmission, for example, a controller produces a digital speed signal based on the output of a shaft speed sensor, and then determines the acceleration of the shaft by computing the derivative of the speed signal. In such an application, conventional derivative calculations are problematic due to the presence of spurious noise in the measured signal, as the derivative of the noise is typically much larger than the derivative of the signal. The usual approach is to low-pass filter either the input signal or its derivative to remove or severely attenuate the noise-related component. However, the filtering introduces phase-delay, which is particularly undesirable if the derivative is to be used for control purposes. Accordingly, what is needed is a way of effectively determining the derivative of a noise-containing input signal without introducing any significant phase delay.